Question

Demostrar identidad trabajando un lado: ( (senθ) / (senθ + cosθ) ) = ( (1) / (1-ctgθ) )

Answer 1

$\textbf{Demostrar: } \dfrac{\sin\theta} {\sin\theta + \cos\theta} = \dfrac {1 } {1+\cot\theta} \\ \\ \\ \textbf{Demostraci\'on}\\ \\ \\ E=\dfrac{\sin\theta} {\sin\theta + \cos\theta}\\ \\ \textit{Para \sin\theta \neq 0 :}\\ \\ E=\dfrac{\dfrac{\sin\theta}{\sin\theta}} {~~~\dfrac{\sin\theta + \cos\theta}{\sin\theta}~~~}\\ \\ \\ E=\dfrac{1}{\dfrac{\sin\theta}{\sin\theta}+\dfrac{\cos\theta}{\sin\theta}}\\ \\ \\ \boxed{E=\dfrac{1}{1+\cot \theta}}$

$\text{En realidad...}\\ \\ \\ E=\begin{cases} \dfrac{1}{1+\cot\theta}&\text{Para }\theta\neq 2k\pi~ ,~\forall k\in\mathbb Z\\ \\ ~~~~~0&\text{Para }\theta =2k\pi~ ,~\forall k\in\mathbb Z \end{cases}$